Problema Solution
a tin maker converts metallic box into 11 cylindrical tins. side of the cube is 51 cm and radius of the cylinder is 7 cm. find the height of each cylinder so made, if the wastage of 12% is incurred in the process.
Answer provided by our tutors
let
h = the height of the a cylinder
r = 7 cm the radius of the cylinder
a = 51 cm the radius of the cube
pi = 3.14
the area of the cube is A cube = 6*a^2 = 6*51^2 = 15606
the area of 1 cylindrical tin is A tin = 2*(r^2)pi + 2r pi * h = 2pi(r^2 + r*h)
the are of 11 cylindrical tins is 11 A tin = 11* 2pi(r^2 + r*h) = 22 pi(r^2 + r*h) = 22*3.14(7^2 + 7h)
the wastage of 12% is incurred in the process that is
(A cube - 11 A tin)/ A cube = 0.12 multiply both sides by A cube
A cube - 11 A tin = 0.12 A cube
11 A tin = A cube (1 - 0.12)
11 A tin = 0.88 A cube
22*3.14(7^2 + 7h) = 0.88*15606
by simplifying and solving the equation we find
h = 21.4 cm is the height of each cylinder made
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